I recently upgraded a Cisco Call Manager environment from 10.5.1 to 10.5.2, and since I had to figure out all the upgrade steps, I figured I'd post my process.  I used the upgrade guide found here: Cisco Upgrade Guide

1. Login to CM Publisher Disaster Recovery System
   a. Backup -> Backup Device -> Add New (if not already present)
   b. Backup -> Manual Backup -> All features -> Start Backup
2. Login to Unity Disaster Recovery System
   a. Backup -> Backup Device -> Add New (if not already present)
   b. Backup -> Manual Backup -> All features -> Start Backup
3. Backup all virtual machines (I used XSI backup to do this)
4. Snapshot all virtual machines within VMware
5. Stop LDAP sync interval on Call Manager and Unity (I use UDS for IM)
   a. This is recommended so that LDAP doesn’t attempt to sync during the upgrade
6. Stop Extension Mobility service -> CM Pub and Sub -> Cisco Unified Serviceability
7. Login to CM Pub, Unity Pub and IM&P Pub
   a. OS Administration -> Software Upgrades -> Remote filesystem (or DVD drive)
   b. Upload new iso and click “Do not reboot after Upgrade”
8. Wait for the all the Pub’s to load the new ISO
9. Login to CM Sub, Unity Sub, and IM&P Sub
   a. OS Administration -> Software Upgrades -> Remote filesystem (or DVD drive)
   b. Upload new iso and click “Do not reboot after upgrade”
10. Login to CM Pub
    a. OS Administration -> Settings -> Version -> Switch Version
    b. Wait for Pub to come back up
11. Login to CM Sub
    a. OS Administration -> Settings -> Version -> Switch Version
    b. Wait for Sub to come back up
12. Check database status
    a. SSH to CM Pub: utils dbreplication runtimestate - value should be “2”
13. Check phone functionality
14. Check version via cli: show version active
15. Verify Extension Mobility service is running
16. Done upgrading Call Manager!
17. Login to Unity Pub
    a. OS Administration -> Settings -> Version -> Switch Version
18. Wait for Unity Pub to come back up, try checking voicemail from a phone
19. Login to Unity Sub
    a. OS Administration -> Settings -> Version -> Switch Version
20. Check database status
    a. SSH to Unity Pub: utils dbreplication runtimestate - value should be “2”
21. Done upgrading Unity!
22. Login to CM Pub and disable IM HA: System -> Presence Redundancy Groups
23. Login to IM&P Pub
    a. OS Administration -> Settings -> Version -> Switch Version
    b. This server took a while to come back up, it has to wait for the Cisco DB to initialize and then the rest of the services will start up
24. Wait for IM&P Pub to come back up with all services started
25. Login to IM&P Sub
    a. OS Administration -> Settings -> Version -> Switch Version
    b. This server also took a while to come back up, it has to wait for the Cisco DB to initialize and then the rest of the services will start up
26. Check database status
    a. SSH to IM&P Pub: utils dbreplication runtimestate - value should be “2”
27. Log into CM Pub and turn on HA for IM cluster
    a. HA will take a couple minutes to re-initialize
28. Done upgrading IM&P!
29. Re-enable LDAP sync on Call Manager and Unity

The upgrade went pretty smoothly, with only one hiccup.  After I upgraded the Unity Pub, I couldn't access the Unity Sub webpage in order to switch the version and upgrade.   The webpage just wouldn't load.  I could have restarted Tomcat and tried to get the webpage working, but I decided to proceed with the upgrade, and switched the version from cli with: utils system switch-version. The upgrade was successful and the entire environment is working great!